**Team Decision: **As discussed in Part 1, it is commonly viewed that taking half after starting on defense results in a team getting a “free break.” *So if you’re a big underdog, does it make sense to pull to start the game in order to have a chance at this “free break?”*

**Takeaway: **No. Start the game on offense even if you are an underdog.

The plot below shows the win probabilities for underdog teams in game simulations based on if they pull or receive to start the game. Each game is played to 15 and does not have an upwind/downwind component. For each scenario, the underdog team’s offensive probability to score each point is 20% less than the favorite team. For example, if the favorite team has a probability to score 60% on each offensive point, then the underdog team has a 40% probability to score each of their offensive points. Another example is the favorite team has a 85% probability to score each of their offensive points and the underdog team has a 65% probability to score each of their offensive points.

It is still better for underdogs to start the game on offense as opposed to pulling. The difference in game win probability is close to zero when the teams do not score a high rate of offensive point probability. But there is a significant difference at high offensive rates.

**Simulation Data**

The tables below show the probability of an underdog team winning a game against an opponent with higher probabilities to score offensive points.

*Probability of Winning a Game to 15 — Results*

The first table provides data that show the probability of winning if an underdog team receives the disc to start the game. The second table provides data that show the probability of winning if an underdog team pulls the disc to start the game. The third table provides the difference in win probabilities for the underdog team if they are receiving to start the game compared to pulling to start the game.

A diagonal in the table is bolded to show game outcomes where the favorite team has a 20% higher offensive hold probability than the underdog. These games have a probability of the favorite winning the game typically between 85–90% of the time. I would categorize these games as ones where the underdog is trying to pull a big upset.

The results in the third table show no statistically significant advantage for underdogs to pull to start a game in any scenario. The trend in the data show that it is still better for underdogs to receive the disc to start the game even if they are trying to pull a big upset.

*How to read the tables?*

**Columns**— Each column corresponds to the favorite team’s probability to score each point that they start on offense going. For example, the “0.90” column simulates games where the favorite team has a 90% probability of scoring every offensive point.**Rows***—*Each row corresponds to the underdog team’s probability to score each offensive point. For example, the “0.60” row simulates games where the underdog team has a 60% probability of scoring every offensive point.**Values (Tables 5.1 & 5.2)***—*The data in each cell of the table show percentage of simulated games that the**underdog team wins**based on both teams’ probability to score each downwind offensive point and upwind offensive point. Each scenario was simulated 250,000 times.**Values (Table 5.3)***—*The data in each cell of the table show the difference in underdog win probability for a given scenario if the underdog team receives compared to pulls to start the game. The data in Table 5.1 and Table 5.2 are used to calculate Table 5.3.

*Notes*

- The reason for the cone shaped tables is that the underdog team’s offensive probability per point should not exceed the favorite team’s and the underdog team’s offensive probability to score should not be less than (1 — favorite team’s offensive probability). For example, if the favorite team scores an expected 70% of their offensive points that means that the underdog team scores 30% of their defensive points. It doesn’t make sense to simulate games where their underdog offensive point probability is less than their defensive point probability.
- There is no upwind/downwind component to the game.
- The values in the tables are estimates of what the true probability is for each scenario. For each scenario, 250,000 games were simulated and therefore the values in the tables have a 95% confidence interval of +/- 0.2% when the win probability is 50%.
- If a favorite has an 85% probability of scoring an offensive point, this can be approximated by rolling a die every point. If the die lands on a “1”, the favorite team is broken. All other die outcomes result in the favorite team scoring their offensive point (83.3%). The same can be said for approximating an underdog team with a 65% probability of scoring an offensive point. If the die lands on “1” or “2”, the underdog team is broken on that offensive point (66.6% offensive hold probability). The simulations repeat this process for every offensive point for every game to determine the win probability for a game scenario. The 85% probability does not mean that the favorite team scores exactly 85% of its offensive points every game in the simulations.

*Reading the Tables — Example*

- Think of a game where the favorite team scores an expected 85% of their offensive points and the underdog team scores an expected 65% of their offensive points. In Table 5.1, the simulations show that the underdog team wins 9.6% of the games when receiving to start the game. In Table 5.2, the simulations show that the underdog team wins 8.7% of the games when pulling to start the game. This difference is only 0.9%, but when considering the low probability of pulling an upset, moving the needle from 8.7% to 9.6% is a significant change.

*Analysis*

From these results, a few things came to mind.

- As shown in the previous parts to this series, the impact of the flip is much more impactful when both teams have higher probabilities to score each offensive point.
- The simulation results do not factor in any psychological impact of taking half after starting the game pulling. The psychological effects in a game of mismatched teams can really make a difference in the effort and probability of achieving an upset.

**Additional Data**

In addition, I added the following three tables for games played to 13 as opposed to 15. As you would expect, the same trend is apparent.

*Probability of Winning a Game to 13 — Results*

**Selection Bias — Taking Half + Winning**

Something to consider when trying to match these results to your intuition is selection bias. When underdog teams start on defense and take half, they are more likely to win compared to a team starting on offense and taking half. This is obvious but I think this may push some to believe that starting on defense is better than starting on offense when trying to pull an upset. It may be due to their selective recollection of winning games when they took half starting on defense. Here’s a breakdown to think about this further.

For the 250,000 simulations in the tables (game to 15 or 13 — Underdog team receiving and pulling), the following are the probabilities of each team taking half, winning if the team takes half, and winning all games.

For both scenarios of games to 15 and 13, the underdog team sees a 9–10% increase in winning a game if they take half when starting on defense compared to taking half when starting on offense. But when you consider the likelihood of taking half in these game scenarios, the underdog team’s probabilities to win the game are still higher when choosing to start the game on offense.

This has been a lot to take in. For Conclusions, check out **Part 6**.